Fracture reduction path planning method and device

Abstract

The application discloses a fracture reduction path planning method and device, and the method comprises the following steps: step 1, determining the initial pose of a fracture fragment and a reduction target pose; step 2, creating a forward random expansion tree and a backward random expansion tree based on the initial pose and the reduction target pose, and performing bidirectional expansion through a RRT-Connect algorithm to obtain an initial reduction path; and step 3, based on a constraint space determined according to the initial reduction path, performing iterative optimization on the initial reduction path through an improved BIT algorithm to obtain an optimized path. The method can realize fast and stable path planning of complex fracture fragments in a high-dimensional space and avoid redundant calculation caused by high-dimensional sampling.

Description

Technical Field

[0001] This invention belongs to the field of fracture reduction technology, specifically, it relates to a fracture reduction path planning method and device. Background Technology

[0002] Preoperative path planning for fracture reduction is crucial for robot-assisted surgery. Taking pelvic fractures as an example, traditional preoperative path planning often uses A / B-based methods. The algorithm's approach, while capable of finding a relatively optimal path in the discrete search space, suffers from the "curse of dimensionality" as the state dimension increases, with the computational cost increasing exponentially with the dimension.

[0003] In recent years, path planning algorithms based on random sampling have emerged, such as Rapidly-exploring Random Tree (RRT) and RRT2. And its extended algorithms, etc. These methods randomly sample and expand the search tree in the search space. Although they have a certain degree of randomness, they are less sensitive to dimensionality, and the computational cost does not increase exponentially with increasing dimensionality. In particular, the RRT algorithm possesses asymptotic optimality, gradually optimizing the path as sampling increases, eventually converging to the optimal solution (probabilistic completeness). To improve efficiency, RRT-Connect, Informed RRT, and other similar algorithms have emerged. FMT BIT Improved algorithms such as AIT have been developed. Existing research has attempted to apply random sampling methods to fracture reduction path planning, for example, by designing Enhanced RRT (ERRT). The algorithm, combined with path shortening technology, can quickly generate pelvic fracture reduction paths and improve path consistency.

[0004] On the other hand, because the fracture models tested are relatively simple (such as iliac wing fractures and sacroiliac joint dislocations), the search efficiency and result quality of such methods are difficult to guarantee for more complex fracture types. In existing semi-automatic planning methods, doctors often follow an empirical strategy of "pulling apart - aligning the posture - translating and reducing" when manually setting the intermediate reduction posture. The path is circuitous and lengthy and causes great stretching to surrounding tissues, which is not conducive to intraoperative safety.

[0005] In summary, there is an urgent need for a fracture reduction path planning method that can efficiently search a six-degree-of-freedom space and adapt to highly complex fractures. Summary of the Invention

[0006] To achieve the above objectives, the present invention provides a method for fracture reduction path planning, comprising: Step 1: Determine the initial position and target position of the fracture fragments for reduction; Step 2: Based on the initial pose and the reset target pose, create a forward random expansion tree and a backward random expansion tree, and then use RRT (Real-Time Tree) to achieve the desired result. The Connect algorithm performs bidirectional expansion to obtain the initial reset path; Step 3: Based on the constraint space determined according to the initial reset path, improve the BIT. The algorithm iteratively optimizes the initial reset path to obtain an optimized path.

[0007] Another aspect of the present invention provides a fracture reduction path planning device, comprising: The attitude setting module is used to determine the initial pose of the fracture fragments and the target pose for repositioning. The initial reset path acquisition module is used to create a forward random expansion tree and a backward random expansion tree based on the initial pose and the reset target pose, and to achieve this through RRT. The Connect algorithm performs bidirectional expansion to obtain the initial reset path; The path optimization module is used to improve the BIT based on the constraint space determined according to the initial reset path. The algorithm iteratively optimizes the initial reset path to obtain an optimized path.

[0008] The beneficial effects of this invention are as follows: (1) Using an improved RRT in a six-degree-of-freedom space -Connect performs bidirectional expansion, including directional expansion, target-guided random expansion, and directional expansion pointing to new nodes. It also performs parent node reselection and rewiring operations on new nodes, enabling fast and stable initial repositioning path search for complex fracture fragments in high-dimensional space.

[0009] (2) Based on improved BIT The algorithm defines the hyperellipsoidal constraint space by the initial reset path, generates batch candidate nodes along the initial reset path, and performs iterative optimization on the candidate node set using an improved heuristic search to obtain a near-optimal reset path. This optimization method can improve path quality and search efficiency, and avoid redundant calculations caused by high-dimensional sampling.

[0010] (3) This method uses a collision detection algorithm based on a hierarchical bounding sphere and a LOS path smoothing optimization algorithm to improve path safety and executability, and realize the clinical applicability and automation of fracture reduction path.

[0011] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0012] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same components in the exemplary embodiments of the invention.

[0013] Figure 1 A flowchart of a fracture reduction path planning method according to an embodiment of the present invention is shown.

[0014] Figure 2 A method for directional expansion of new nodes is shown in a fracture reduction path planning method according to an embodiment of the present invention.

[0015] Figure 3 A goal-guided random expansion of new nodes is shown as an embodiment of the fracture reduction path planning method according to an embodiment of the present invention.

[0016] Figure 4 A method for directional expansion of new nodes to a new node is shown in a fracture reduction path planning method according to an embodiment of the present invention.

[0017] Figure 5 A method for reselecting the parent node is shown in a fracture reduction path planning method according to an embodiment of the present invention.

[0018] Figure 6 A rewiring method for a fracture reduction path planning method according to an embodiment of the present invention is shown.

[0019] Figure 7 A method for smoothing LOS in a fracture reduction path planning method according to an embodiment of the present invention is shown.

[0020] Figure 8 A node distance optimization method for a fracture reduction path planning method according to an embodiment of the present invention is shown.

[0021] Figure 9 A fracture reduction path planning method according to an embodiment of the present invention is shown, which generates batch nodes within a constraint space.

[0022] Figure 10 The initial reduction path and expanded nodes obtained by a fracture reduction path planning method according to an embodiment of the present invention are shown.

[0023] Figure 11 The initial pose and target pose of the fracture fragments in a fracture reduction path planning method according to an embodiment of the present invention are shown.

[0024] Figure 12 The search space of a fracture reduction path planning method according to an embodiment of the present invention is shown.

[0025] Figure 13 An optimized path after multiple iterations of a fracture reduction path planning method according to an embodiment of the present invention is shown. Detailed Implementation

[0026] Preferred embodiments of the invention will now be described in more detail. While preferred embodiments of the invention are described below, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0027] like Figure 1 As shown, this invention relates to a method for planning fracture reduction paths, comprising: Step 1: Determine the initial position and target position of the fracture fragments for reduction; Step 2: Create a forward random expansion tree and a backward random expansion tree based on the initial pose and the reset target pose, using RRT. The Connect algorithm performs bidirectional expansion to obtain the initial reset path; Step 3: Based on the constraint space determined according to the initial reset path, improve the BIT. The algorithm iteratively optimizes the initial reset path to obtain the optimized path.

[0028] The following is a detailed explanation of each step.

[0029] Step 1: Determine the initial position of the fracture fragments and the target position for reduction.

[0030] Before path planning, it is necessary to determine the initial pose of the fracture fragments and the target pose for reduction. The initial pose can be obtained by segmenting and reconstructing the patient's CT images using 3D-UNet. The target pose for reduction is derived from the expected fracture reduction pose given in relevant studies, such as the expected fracture reduction pose given by Statistical Shape Model (SSM) matching.

[0031] by Indicates the initial pose, where , Indicates the initial position. Indicates the initial attitude.

[0032] by Indicates the reset target pose, where Indicates the target reset position. This indicates the reset target attitude.

[0033] In this invention, and The centroid (mean of all points) of the point cloud of the fracture fragment model under the initial pose and the target pose of the reduction state. This is the rotation vector transformed from the rotation matrix from the initial pose to the target pose. First, principal component analysis (PCA) is used to obtain the 3D principal axes of the fracture fragment model point clouds in both the initial and target poses, thus obtaining the rotation matrix from the initial pose to the target pose, which is then converted into axis-angle parameters. Alternatively, the transformation matrix can be obtained directly through iterative nearest point (ICP) registration.

[0034] Step 2: Create a forward random expansion tree and a backward random expansion tree based on the initial pose and the reset target pose, using RRT. The Connect algorithm performs bidirectional expansion to obtain the initial reset path.

[0035] RRT The Connect algorithm is a method that integrates RRT... This invention employs a sampling planning algorithm that combines optimal asymptotic convergence with the efficient bidirectional expansion strategy of RRT-Connect, primarily used to solve optimal path planning problems in high-dimensional spaces. Depending on the specific application scenario, this invention selects either directional expansion directly pointing to the target pose or target-guided random expansion to accommodate situations where there are varying numbers of obstacles within the skeleton. Furthermore, for new nodes added during expansion, the expansion tree is optimized by reselecting parent nodes and rewiring to shorten the path as much as possible. Step 2 includes the following specific steps.

[0036] Step 21: Create a forward random expansion tree with the initial pose as the root node, and create a reverse random expansion tree with the reset target pose as the root node.

[0037] The forward random expansion tree and the backward random expansion tree created in this step both contain only the root node. In subsequent steps, the forward random expansion tree and the backward random expansion tree expand nodes outward from the root node until they are connected to each other.

[0038] Step 22: Expand the current tree with new nodes by at least one of the following: directed expansion directly to the target, random expansion based on the target, and directed expansion to the new node. The current tree is one of the forward random expansion tree and the reverse random expansion tree.

[0039] Before expanding, the search space, search step size, and average step size are calculated first.

[0040] To achieve six-degree-of-fact reset path planning, this invention employs a sampling-based search method with low sensitivity to high-dimensional searches. This search first requires determining the range of the search space. Determining the search space requires a balance between efficiency and accuracy. On the one hand, the search space should be large enough to cover as many feasible paths as possible; on the other hand, an excessively large search space will reduce computational efficiency. To achieve this balance, in this invention, the search space is a sphere with the midpoint between the initial position and the reset target position as its center and a radius equal to a multiple of the distance between the initial position and the reset target position. The formulas for calculating the center position and radius of the search space are as follows: k

[0041] in, Represents the radius of the search space. This indicates the center position of the sphere in the search space, and k represents the scaling factor, which can be set according to actual needs (e.g., 1.5).

[0042] The search step size includes the translation step size. and rotation step size Calculated according to the following formula:

[0043] in, NS This indicates the preset number of steps.

[0044] Since the initial pose and the target pose for reduction are determined based on the centroids of the fracture fragment model point cloud in their initial and target states, the search space and search step size also depend on their centroids. The advantages of determining the search space and search step size using the centroid of the model point cloud are: first, fracture reduction requires balancing mechanical loads, and the centroid path is more consistent with physiological movement and has biomechanical rationality; second, the movement of the centroid can better reflect the overall movement of the fragments and avoid collisions with local protrusions.

[0045] Calculate the average step size using the following formula. :

[0046] in, Points on the point cloud of the fracture fragment model in the initial pose. To start from the initial pose Reset target pose A 3x3 rotation matrix, num This represents the number of points in the point cloud. The average step size is also used to determine multiple search ranges and thresholds in subsequent calculations.

[0047] Then, a new node is added to the current tree through at least one of the following methods: directional expansion directly pointing to the target, random expansion guided by the target, or directional expansion pointing to the new node. Specifically, the strategy is as follows: first, a new node is added to the current tree through directional expansion directly pointing to the target; if this fails, a new node is added through directional expansion pointing to the new node; if this also fails, a new node is added through random expansion guided by the target. Here, expansion failure refers to a collision in the path from the current node to the new node.

[0048] (1) Directed expansion directly targeting the target

[0049] To improve efficiency, a targeted expansion method that directly points to the target can be used. Random probabilities are set. rand , rand Greater than zero and less than 1. When rand When the value is less than a certain fixed value (e.g., 0.5), the current root node of the tree is used. or () as the initial pose for this extension The root node of another extended tree ( or () as the target pose for this expansion Using the current node in the current tree that needs to be expanded Expand the parent node. During the expansion process, directly expanding based on fixed translation and rotation step sizes may not be sufficient to expand from the parent node to the target pose; therefore, an average step size is used. Calculation from arrive The number of steps, through uniform translation and rotation, yields a new pose, which serves as the new node. .

[0050]

[0051] in, It is a rounding function. From arrive A 3x3 rotation matrix, From arrive A 3x3 rotation matrix, From arrive The distance between them From arrive The distance. As mentioned above, all poses are determined by the centroid of the point cloud of the fracture fragment model.

[0052] Figure 2Showing an example of the results of directional expansion, where the root node of the tree is expanded from the other side ( or (as target pose) Search for the distance from the current tree The nearest node As the current node, expand using this node as the parent node, towards... Forward .

[0053] (2) Goal-guided stochastic expansion

[0054] when rand When a node cannot be expanded due to a collision in a directional expansion that is greater than a certain fixed value (e.g., 0.5) or directly towards the target, a target-guided random expansion is performed. Traditional RRT algorithms randomly select points in the search space and then find the nearest point in the expansion tree, moving from the nearest point towards that point. However, to ensure the search space covers all feasible paths, this invention sets the search path to be relatively large, resulting in a large number of invalid and redundant search nodes from completely random expansion. To improve search efficiency, this invention introduces a directional guidance vector pointing towards the target to increase expansion in the target direction. In this way, new nodes are calculated according to the following formula:

[0055] in, Represents a random point in the search space. Represents the coefficients of a random vector. This represents the target guiding vector coefficient. It is worth noting that when... and When equal, move away Vectors that are at an angle greater than 90 degrees to the vector are completely discarded. To avoid this, in this embodiment, and The ratio is set to 2.

[0056] Figure 3 Showing an example of results for a goal-guided random expansion, where from the current node... To the new node The direction vector is composed of 2 / 3 arrive The direction vector and 1 / 3 arrive It is composed of directional vectors.

[0057] (3) Directed expansion to new nodes

[0058] To further improve efficiency, this invention draws on the highly efficient RRT-Connect method. Unlike the traditional RRT method, which generates only one tree, RRT-Connect performs random tree expansion at both the start and end points, generating new nodes in a tree as needed. Then, find another tree that is closer to the new node. The most recent node is used as the current node to be expanded. Calculate new nodes according to a directional expansion method that directly points to the target, so as to... Towards Expand. If a direct connection can be found, the two trees are connected, meaning a collision-free path has been found. If a collision occurs during the expansion process, the expansion process restarts.

[0059] The specific node expansion method is similar to that in (1), firstly by using the average step size Calculation from arrive The number of steps is used to determine the specific translation and rotation step sizes. Then, based on the calculated translation and rotation step sizes, the nodes are oriented and expanded until the desired result is reached. Complete path planning, or stop directional expansion and re-expand if a collision occurs.

[0060] Figure 4 This shows an example of the result of a directional expansion pointing to a new node. The expansion method is similar to a directional expansion directly pointing to a target, generating nodes in a tree. Then, find another tree that is far from that node. The nearest node Based on the directional expansion method from the parent node Towards It continues to grow, thereby acquiring new nodes. until connected Complete the connection between the two trees or re-expand if a collision is detected.

[0061] In this invention, directional expansion directly pointing to the target, directional expansion pointing to a new node, and target-guided random expansion are selected sequentially. This improves expansion efficiency and is applicable to situations where various obstacles exist within the bone. In fracture reduction procedures, fracture fragments typically need to avoid internal bone structures and align with the fracture surface; a straight path directly towards the reduction target pose is usually not feasible. Therefore, this invention combines random vectors with target-guided vectors to allow expansion to explore directions other than the target pose while still moving towards it. This allows for the exploration of curved paths that bypass obstacles (internal bone structures), making it more suitable for scenarios with complex internal bone structures.

[0062] Step 23: Re-determine the parent node for the new node to minimize the path cost from the root node of the current tree to the new node.

[0063] Since most nodes on the randomly expanded tree are generated based on random search, for a new node generated with the current node as the parent node, its path may be redundant and the path cost may be large. Therefore, by reselecting the parent node, possible parent nodes around the new node are searched to minimize its path cost.

[0064] First, determine the search area for parent node search, which can be a spherical area centered on the new node with a preset radius as the search radius. The preset radius can be based on the average step size in Step 22 to determine. For example, it can be set as a multiple of the average step size of.

[0065] Then, search for nodes within the search area among all nodes of the current tree as candidate parent nodes. Next, for each candidate parent node, check whether the path from it to the new node has a collision. If there is no collision, calculate the path cost from the root node of the current tree to the new node through the candidate parent node. The path cost between two nodes is usually the distance or weighted distance between the two nodes. Finally, calculate the path cost from the root node of the current tree to the new node through the original parent node of the new node, compare it with the minimum path costs of all candidate parent nodes. If the latter is less than the former, take the candidate parent node corresponding to the minimum path cost as the new parent node of the new node.

[0066] Figure 5 shows an example of the result of reselecting the parent node. In the figure is the reselected parent node for the new node After reselecting the parent node, the path length from the starting point to the new node becomes shorter.

[0067] By reselecting the parent node, through local and low-cost adjustments, global progressive optimization of the path can be achieved, and a path closer to a straight line (or minimum energy) can be found. For fracture reduction operations, a shorter path means less movement distance of fracture fragments, and less traction and damage to surrounding muscles, blood vessels, and nerves. The path optimized in this way is usually smoother, the reduction operation is simpler, and the operation time can be shortened.

[0068] Step 24: For each neighboring node of the new node, compare the path cost c1 from the root node of the current tree through the new node to the neighboring node with the original path cost c2 from the root node of the current tree to the neighboring node. If c1 < c2 and there is no collision in the straight-line path from the new node to the neighboring node, perform a re-wiring operation to make the new node the parent node of the neighboring node.

[0069] First, define a neighboring range, which is usually the same as the search area in step 23 to ensure the consistency of optimization. Then, find the nodes within the neighboring range among all the nodes of the current tree as neighboring nodes, but the parent node of the new node finally determined in step 23 is usually excluded. Next, for each neighboring node, calculate the path cost c1 from the root node of the current tree through the new node to the neighboring node and the original path cost c2 from the root node of the current tree to the neighboring node, and compare c1 and c2; if c1 < c2 and there is no collision on the straight-line path from the new node to the neighboring node, perform a re-wiring operation to make the new node the parent node of this neighboring node. As mentioned above, the path cost between two nodes is usually the distance or weighted distance between the two nodes. In this step, the aforementioned collision detection method based on hierarchical bounding spheres is still used to determine whether there is a collision on the path.

[0070] Figure 6 Shows an example of the result of re-wiring. In the figure, through re-wiring, the new node becomes the parent node of its neighboring node After re-wiring, the path length from the starting point to the neighboring node becomes shorter.

[0071] The re-wiring operation can continuously optimize the structure of the expanding tree, ensuring that the overall path cost (such as the moving distance of fracture fragments, soft tissue damage, etc.) from the initial pose to the reset target pose remains minimized. In a complex anatomical environment, a path that seems locally shorter may be longer or pass through high-risk areas globally. The re-wiring operation can dynamically connect neighboring nodes to more optimal parent nodes, thereby generating a smoother, shorter total movement, and more efficient reset path.

[0072] In step 23, whenever a new node is added, a parent node with a lower path cost is searched nearby, which ensures that the new node itself is connected to the tree in an optimal way, that is, with the minimum cost, thus achieving local optimization of the path. In step 24, after adding a new node, it is checked whether it can become a more optimal parent node of other existing neighboring nodes, thereby optimizing the connections of the existing parts in the tree and further achieving global optimization. By combining steps 23 and 24, the new nodes can be continuously used to correct and optimize the entire path, so as to find the globally optimal or near-optimal path within a limited time.

[0073] Step 25: Repeat steps 22 to 24 until the forward random expanding tree and the backward random expanding tree are connected, thereby obtaining the initial reset path.

[0074] According to a preset strategy, one tree from the forward random expansion tree and the backward random expansion tree is selected as the current tree to be expanded in this round. Steps 22 to 24 are repeated until the forward random expansion tree and the backward random expansion tree are connected. In this invention, when the distance between the forward random expansion tree and the backward random expansion tree is less than a preset threshold, they are considered connected, and expansion stops. Generally, the preset threshold is set as the average step size. At this point, a discrete path is formed from the initial pose to the reset target pose, namely the initial reset path, denoted as [S0, S1, ... S]. end ], where S0= S end = .

[0075] It is worth noting that since the initial reset path is obtained by random expansion guided by the target, it is a zigzag path composed of a series of discrete points, which usually contains a lot of redundancy. As a preferred solution, after step 2, the initial reset path is smoothed by the LOS (Line-of-Sight) algorithm.

[0076] The core of the LOS algorithm is to check whether there exists a collision-free straight path (line of sight) between two points. Specifically, taking the starting point S0 of the initial reset path as the current node, and the path ending point S... end Connect the lines, and on the connecting lines... The threshold is determined by uniformly sampling points in the same way as the directional expansion directly pointing to the target, and judging whether there is a collision in the intermediate path; if there is no collision, it indicates that S0 and S... end If there is a direct path between them, delete all intermediate nodes [S1, S2, ..., S...]. end-1 The process is complete. If a collision occurs, it indicates that a direct route is not possible. Connect the starting point S0 with the second-to-last node S. end-1 Repeat the above process. After the starting point S0 is detected, push one node backward from that side (using the shortened path; if the shortened path is S4 after S0, then push it backward to S4) until the current node is the end point of the initial reset path, thus completing the smoothing post-processing.

[0077] Figure 7 The example of the LOS smoothing result is shown, where red dots represent the start and end points, blue broken lines represent the initial reset path, blue dots represent intermediate nodes of the path, green broken lines represent the path after LOS smoothing, and yellow asterisks represent intermediate nodes where points are evenly selected between nodes to detect whether a collision occurs between two nodes.

[0078] Through iterative processes, the number of inflection points in the initial reduction path can be significantly reduced, unnecessary detours in the path can be removed, and two directly reachable pose nodes can be directly connected, shortening and simplifying the path. In tests, after LOS processing, the number of intermediate nodes in the initial reduction path can be reduced from approximately 10 to 2, the path length is significantly shortened, and the movement process is smoother. The unique advantages of the LOS algorithm in fracture reduction are: first, the anatomical reduction principle usually adopts the shortest anatomical path, and the ideal reduction path is usually close to a straight line; second, linear motion provides more uniform traction to soft tissues.

[0079] In the aforementioned steps, a collision detection method based on hierarchical bounding spheres is employed to ensure that the generated paths do not cause interference or collisions between the fracture fragments and surrounding bone. This method utilizes hierarchical bounding spheres of the 3D model of the fracture fragments for rapid collision detection. First, for each surface triangular facet of the 3D model of the fracture fragments, a bottom-level bounding sphere is constructed with its centroid as the center. The bottom-level bounding sphere is the smallest bounding sphere that tightly encloses the triangular facet. Then, an improved K-means clustering method is used to generate multiple layers of bounding spheres from bottom to top.

[0080] During collision detection, a coarse screening process is first performed on large spheres at higher levels, refining the detection layer by layer. When the bottommost enclosing sphere is detected, a fine intersection test is conducted on the corresponding triangular facets, thus ensuring both detection accuracy and efficiency. This layered collision detection method can quickly locate potential collision points and ultimately determine whether a collision exists on the path through precise triangular facet intersection tests.

[0081] Furthermore, this invention requires extensive computation of distances between nodes. Due to the large size and rich detail of fracture fragments, the number of points in the model's point cloud is large. When there are many nodes in the expanded tree, the computational load for a single nearest node and threshold node search is very high. Therefore, this invention optimizes node distance calculation through hierarchical distance calculation. Figure 8 As shown, firstly, the distance between the centroids of the point cloud in the node model is calculated to roughly estimate its effective distance (the average distance of the point cloud is usually greater than the distance between the centroids); then, nodes with a distance of 1.5 from the current node are selected. We perform fine-grained point cloud distance calculations on points within a certain range. This improves computational efficiency and avoids calculation errors caused by rough estimations. Figure 8 In the process, to calculate and filter the distance between the current node (green dot) and its surrounding nodes, first calculate the distance between the current node and the centroid of each node, then for the light blue dashed circle (with a distance of 1.5), Perform fine point cloud distance calculations on nodes within a radius to obtain the precise distance between nodes.

[0082] Step 3: Based on the constraint space determined according to the initial reset path, improve the BIT. The algorithm iteratively optimizes the initial reset path to obtain an optimized path.

[0083] Due to RRT -Connect's path search exhibits high randomness; even after LOS smoothing, the generated paths typically retain some randomness. Although this invention uses parent node reselection and rerouting operations to achieve incremental optimization, the large search space set during initial expansion to ensure a solution makes incremental optimization very inefficient, with most randomly generated nodes falling outside the optimization range. To further optimize the generated paths, this invention employs an improved BIT... The (Batch Informed Tree) algorithm optimizes the initial reset path, combining the advantages of sampling-based and heuristic search-based algorithms: First, it randomly samples the entire solution space to obtain an initial path through a heuristic function; then, to improve search efficiency, it sets a hyperellipsoidal constraint space with the length of the initial path as the major axis to narrow the search space. Batch sampling is performed within this constraint space to obtain randomly generated batch nodes. The aforementioned heuristic search-based path generation method is repeated to obtain a new path based on these batch sampling points, thus achieving path optimization; this process is repeated until the set stopping condition is reached. The following details each sub-step of step 3.

[0084] Step 31: Determine the constraint space, which is a hyperellipsoid with the initial pose and the reset target pose as foci and the length of the initial reset path as the major axis.

[0085] Length of the initial reset path l Calculate using the following formula:

[0086] in, Let i be the three-dimensional coordinates of point i on the point cloud of fracture fragments in state S0. num The number of points in the point cloud. For S j The three-dimensional coordinates of point i in the state.

[0087] The constraint space is the constraint condition for subsequent searches. This strategy narrows the search space, allowing the algorithm to focus on the region related to the initial reset path.

[0088] Step 32: Perform random sampling expansion on the initial reset path to obtain candidate nodes in the constraint space, thereby forming a candidate node set.

[0089] Traditional BIT The previous method directly generated batch sampling points randomly within the ellipsoid. Since it's a two-dimensional plane, it can quickly calculate whether a point is within an obstacle using a set, and use other collision detection methods to determine if collisions occur in subsequent movement paths. However, this invention uses a collision detection method based on a hierarchical bounding sphere, which only detects whether a collision occurs at that specific location, ignoring collision detection during subsequent movement. Furthermore, the path planning method of this invention is based on 6 degrees of freedom, and directly performing uniform random sampling of 6 degrees of freedom in the hyperellipsoidal space requires a large number of samples. Also, if the distance between generated nodes is large, the tunneling effect needs to be considered to calculate collisions during movement. Given that an initial reset path optimized by LOS has been obtained, this initial reset path can be used as prior information for path optimization.

[0090] Step 32 specifically includes: Step 321: Using average step size Calculate the number of interpolation points, and insert intermediate nodes between the nodes of the initial reset path according to the number of interpolation points, so that the distance between adjacent nodes on the initial reset path is less than a first preset value.

[0091] In step 2, the initial reset path obtained through bidirectional expansion of the random expansion tree typically includes only a few turning nodes. In this step, firstly, by averaging the step size... Calculate the number of interpolation points and insert intermediate nodes between nodes to make the distance between adjacent nodes on the path similar, for example, less than a first preset value.

[0092] Step 322: Randomly shift each node on the interpolated path. And rotate around a random axis To generate new nodes, select new nodes that fall within the constraint space as candidate nodes; repeat the operation to obtain several batches of candidate nodes until the number of candidate nodes reaches the second preset value.

[0093] Step 323: Form a candidate node set from the candidate nodes.

[0094] Summarizing the candidate nodes yields the candidate node set (i.e., the informed set), which is used for subsequent path optimization.

[0095] Figure 9 This shows an example of batch nodes generated within the constraint space. The dashed ellipse represents the constraint space, a convenient area for optimizing the search range; all batch nodes used for subsequent path optimization fall within this range. Initial pose. and reset target pose The two foci of the ellipse are represented by the blue line, which is the initial reset path, i.e., the path to be optimized, and its length is the length of the ellipse's major axis. The dark blue dots are the nodes of the initial reset path, and batch processing nodes are generated based on these nodes. The light green dots are the batch processing nodes after the first expansion, and the dark green dots are the batch processing nodes after the second expansion. Figure 10 The initial reset path (blue line) and the nodes in the expanded candidate node set (gray dots) are displayed.

[0096] Step 33: Starting from the initial pose and ending at the reset target pose, perform a heuristic search on the candidate node set to obtain a preliminary optimized path.

[0097] Heuristic search starts from the starting point, expands nodes in all directions with a set step size, and calculates and updates the cost of the expanded nodes using heuristic functions until the search stops near the target location.

[0098] To improve search efficiency, this invention optimizes the weight settings of the heuristic function, appropriately increasing the weight of the estimated cost h from the node to the destination, making the search more goal-oriented while ensuring the rationality of the path cost evaluation, thereby accelerating convergence. Step 33 specifically includes the following sub-steps.

[0099] Step 331: Create and initialize the open list, closed list, non-collision node list, and g-value list.

[0100] First, create an Openlist, a Closelist, a Non-collisionlist, and a Glist of values. The Openlist stores nodes to be expanded, the Closelist stores expanded nodes, the Non-collisionlist stores randomly generated nodes that pass collision detection, and the Glist stores the cumulative cost g of each node. Initially, the Openlist contains only the starting point, the Closelist and Non-collisionlist are empty, and the cumulative cost g of the starting point is zero.

[0101] Step 332: Select the node with the smallest comprehensive cost f from the open list as the current node, and move the current node into the closed list.

[0102] The comprehensive cost f of a node is calculated based on the evaluation function f(x). Where f(x) = g(x) + w h(x), where x represents a node, g(x) represents the cumulative cost function, which is used to calculate the actual cumulative cost from the starting point to node x, and h(x) represents the heuristic function, which is used to calculate the estimated cost from node x to the end point. w represents the heuristic weight. When w > 1, the algorithm approaches the BFS method, is more target-directed, and the overall calculation efficiency is improved. However, since the proportion of the actual path cost is reduced, the generated path becomes longer, and this trend is more obvious as w increases. By comparing the search effects for different w values in the experiment, w = 1.5 is selected.

[0103] Step 333: Check whether the current node is in the non-collision node list. If so, proceed to the next step; otherwise, perform a collision detection on the current node. If there is a collision, return to Step 332 to reselect the current node. If there is no collision, add the current node to the non-collision node list and continue to the next step.

[0104] Step 334: Detect the distance between the current node and the end point. If the distance is less than the distance threshold (taking the average step length ), then jump to Step 337; otherwise, continue to the next step.

[0105] Step 335: Determine the adjacent nodes of the current node and calculate the temporary cost temp for each adjacent node.

[0106] Among them, the adjacent nodes are the nodes in the candidate node set whose distance from the current node is within the preset distance. The preset distance is taken as a multiple of the average step length, such as 1.5 . The temporary cost temp = g(x) + cost(x, neighbor), where x represents the current node, neighbor represents the neighboring node, and cost represents the cost of moving from the current node x to the neighboring node neighbor (usually represented by the distance between nodes). To ensure the calculation accuracy, the distance is calculated in the way of the average distance of the model point cloud.

[0107] Step 336: For each adjacent node, judge whether it is in the g value list. If it is, compare its temporary cost temp with the cumulative cost g saved in the g value list. If temp < g, update the cumulative cost g corresponding to this neighboring node in the g value list, calculate its comprehensive cost f, and update the parent-child relationship between the current node and this adjacent node; for each adjacent node, judge whether it is in the open list. If it is not in the open list, or if it is in the open list and its temporary cost temp is less than its actual cumulative cost g, set the current node as its parent node, move it into the open list, update the cumulative cost g corresponding to this neighboring node in the g value list, and calculate its comprehensive cost f; then, return to Step 332.

[0108] Step 337: Visit the parent node of each node in sequence from the endpoint until backtracking to the starting point to obtain the preliminary optimized path.

[0109] Step 34: Smooth the preliminary optimized path using the LOS algorithm.

[0110] A preliminary optimized path from the starting point to the ending point is obtained through heuristic search. This path is then smoothed using the Loss of Roots (LOS) algorithm to remove unnecessary redundant turns, resulting in a lower curvature. This reduces drastic changes in the posture of the fracture fragments during reduction, thus lowering the difficulty of controlling the surgical robot and reducing impact on the patient's tissues. This smoothing process ensures that the path is both short and smooth, facilitating the robot's fracture reduction operation. The smoothing process using the LOS algorithm has been described previously and will not be repeated here.

[0111] Step 35: Replace the initial reset path with the preliminary optimized path, and repeat steps 31 to 34 until the preset conditions are met.

[0112] The preliminary optimized path, smoothed in step 34, is used as a new candidate solution to replace the initial reset path. Steps 31 to 34 are repeated to continuously approach the optimal path until a preset condition is met, such as the path shortening rate being less than a threshold (e.g., 1%) in two consecutive iterations or the maximum number of iterations is reached. Through iteration, the path will converge to the shortest path, obtaining the final high-quality reset path.

[0113] The present invention also provides a fracture reduction path planning device, comprising: The attitude setting module is used to determine the initial pose of the fracture fragments and the target pose for repositioning. The initial reset path acquisition module is used to create a forward random expansion tree and a backward random expansion tree based on the initial pose and the reset target pose, and to achieve this through RRT. The Connect algorithm performs bidirectional expansion to obtain the initial reset path; The path optimization module is used to improve the BIT based on the constraint space determined according to the initial reset path. The algorithm iteratively optimizes the initial reset path to obtain an optimized path.

[0114] The specific steps and implementation methods of each module have been described above and will not be repeated here.

[0115] Example

[0116] Pelvic fractures are complex fracture conditions, requiring significant rotation and translation of fracture fragments for reduction and reassembly, thus demanding sophisticated path planning. This embodiment uses a pelvic fracture as an example to illustrate the specific steps of the fracture reduction path planning method of the present invention.

[0117] Step 1: Determine the initial pose and the reset target pose of the fracture fragment.

[0118] Segment and three-dimensionally reconstruct the patient's CT image through 3D-UNet to obtain the initial pose. The target pose comes from the expected fracture reduction pose given by the statistical shape model. Figure 11 Display the initial pose (faded green area) and the reset target pose (blue area) of the fracture fragment.

[0119] Step 2: Create a forward random expansion tree and a backward random expansion tree based on the initial pose and the reset target pose, and perform bidirectional expansion through the RRT -Connect algorithm to obtain the initial reset path. Specifically, it includes: Step 21: Create a forward random expansion tree with the initial pose as the root node and a backward random expansion tree with the reset target pose as the root node.

[0120] Step 22: Expand new nodes for the current tree through direct target-oriented expansion, target-guided random expansion, and direct target-oriented expansion to a new node.

[0121] In this embodiment, since it is uncertain whether there is a large range of detours due to the need for collision avoidance during the reset process, the search space is a sphere centered at the midpoint between the initial position and the reset target position and with a radius of 1.5 times the distance between the initial position and the reset target position. Figure 12 Display the search space, represented by a blue translucent sphere. The green, blue, and black points in the figure represent the reset target position, the initial position, and the center of the search space, respectively.

[0122] Step 23: Re-determine the parent node for the new node so that the path cost from the root node of the current tree to the new node is minimized.

[0123] Step 24: For each neighboring node of the new node, compare the path cost c1 from the root node of the current tree through the new node to the neighboring node with the original path cost c2 from the root node of the current tree to the neighboring node. If c1 < c2 and there is no collision in the straight-line path from the new node to the neighboring node, perform a re-wiring operation to make the new node the parent node of the neighboring node.

[0124] Step 25: Repeat steps 22 to 24 until the forward random expansion tree and the backward random expansion tree are connected, thereby determining the initial reset path.

[0125] Step 27: Smooth the initial reset path through the LOS algorithm.

[0126] Step 3: Based on the constraint space determined according to the initial reset path, improve the BIT. The algorithm iteratively optimizes the initial reset path to obtain an optimized path. Step 3 includes: Step 31: Determine the constraint space, which is a hyperellipsoid with the initial pose and the reset target pose as foci and the length of the initial reset path as the major axis; Step 32: Perform random sampling expansion on the initial reset path to obtain candidate nodes in the constraint space, thereby forming a candidate node set; Step 33: Starting from the initial pose and ending at the reset target pose, perform a heuristic search on the candidate node set to obtain a preliminary optimized path; Step 34: Smooth the initially optimized path using the LOS algorithm; Step 35: Replace the initial reset path with the preliminary optimized path, and repeat steps 31 to 34 until a preset condition is met. In this embodiment, the preset condition is that the path shortening length is less than 5% for two consecutive times. Figure 13 This displays the optimized path after multiple iterations. The optimized path is shorter and smoother than the initial reset path.

[0127] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for planning fracture reduction paths, characterized in that, including: Step 1: Determine the initial pose and the reset target pose of the fracture fragment; Step 2: Based on the initial pose and the reset target pose, create a forward random expansion tree and a backward random expansion tree, and then use RRT (Real-Time Tree) to achieve the desired result. The Connect algorithm performs bidirectional expansion to obtain the initial reset path; Step 3: Based on the constraint space determined according to the initial reset path, improve the BIT. The algorithm iteratively optimizes the initial reset path to obtain an optimized path.

2. The fracture reduction path planning method according to claim 1, characterized in that, In step 1, with Indicates the initial pose, where , Indicates the initial position. Indicates the initial attitude; by Indicates the reset target pose, where Indicates the target reset position. Indicates the reset target attitude; Determine the initial position and the reset target position according to the centroids of the point clouds of the fracture fragment models in the initial state and the reset target state.

3. The fracture reduction path planning method according to claim 2, characterized in that, Said Step 2 includes: Step 21: Create the forward random expansion tree with the initial pose as the root node, and create the reverse random expansion tree with the reset target pose as the root node; Step 22: Expand a new node for the current tree by at least one of the direct target-oriented expansion, the target-guided random expansion, and the new node-oriented expansion; Step 23: Re-determine the parent node for the new node so that the path cost from the root node of the current tree to the new node is minimized; Step 24: For each neighboring node of the new node, compare the path cost c1 from the root node of the current tree through the new node to the neighboring node with the original path cost c2 from the root node of the current tree to the neighboring node. If c1 < c2 and there is no collision in the straight-line path from the new node to the neighboring node, perform the re-wiring operation to make the new node the parent node of the neighboring node; Step 25: Repeat Steps 22 to 24 until the forward random expansion tree and the reverse random expansion tree are connected, thereby determining the initial reset path.

4. The fracture reduction path planning method according to claim 3, characterized in that, In Step 22, first expand a new node for the current tree by the direct target-oriented expansion. If the expansion fails, expand a new node for the current tree by the new node-oriented expansion. If the expansion fails, expand a new node for the current tree by the target-guided random expansion; For the direct target-oriented expansion, calculate the new node according to the following formula: For the target-guided random expansion, calculate the new node by the following formula: For a directed expansion pointing to a new node, the node is expanded on an expanded tree. Then, search for distances on another extended tree. The most recent node is used as the current node to be expanded. Calculate new nodes by directional expansion that directly points to the target; in, Indicates a new node. This represents the current node in the tree that needs to be expanded. This represents the root node of the current tree. This represents the root node of another tree. It is a rounding function. From arrive A 3x3 rotation matrix, From arrive A 3x3 rotation matrix, From arrive The distance between them From arrive The distance; Represents a random point in the search space. Represents the coefficients of a random vector. Represents the target guiding vector coefficients; Indicates the average step size: in, Points on the point cloud of the fracture fragment model in the initial pose. To start from the initial pose Reset target pose A 3x3 rotation matrix, num The number of points in the point cloud; Indicates the translation step size. Indicates the rotation step size: in, NS Indicates the preset number of steps; The search space is a sphere with the midpoint between the initial position and the reset target position as the center of the sphere and a multiple of the distance between the initial position and the reset target position as the radius.

5. The fracture reduction path planning method according to claim 1, characterized in that, It also includes: After Step 2, smooth the initial reset path by the LOS (Line-of-Sight) algorithm.

6. The fracture reduction path planning method according to claim 1, characterized in that, Said Step 3 includes: Step 31: Determine the constraint space, which is a hyper-ellipsoid with the initial pose and the reset target pose as the foci and the length of the initial reset path as the major axis; Step 32: Perform random sampling expansion on the initial reset path to obtain candidate nodes within the constraint space, and then form a candidate node set; Step 33: Starting from the initial pose and ending at the reset target pose, perform heuristic search on the candidate node set to obtain a preliminary optimized path; Step 34: Smooth the preliminary optimized path by the LOS algorithm; Step 35: Replace the initial reset path with the preliminary optimized path, and repeat Steps 31 to 34 until the preset conditions are met.

7. The fracture reduction path planning method according to claim 6, characterized in that, Said Step 32 includes: Step 321: Using the average step size Calculate the number of interpolation points, and insert intermediate nodes between the nodes of the initial reset path according to the number of interpolation points, so that the distance between adjacent nodes on the initial reset path is less than a first preset value; Step 322: Randomly shift each node on the interpolated path. And rotate around a random axis To generate new nodes, select new nodes that fall within the constraint space as candidate nodes; repeat the operation to obtain several batches of candidate nodes until the number of candidate nodes reaches a second preset value; Step 323: Form the candidate node set with the candidate nodes.

8. The fracture reduction path planning method according to claim 6, characterized in that, Said Step 33 includes: Step 331: Create and initialize an open list, a closed list, a non-collision node list, and a g-value list; Step 332: Select the node with the minimum combined cost f from the open list as the current node, and move the current node into the closed list; Step 333: Check whether the current node is in the non-collision node list. If so, proceed to the next step; otherwise, perform a collision detection on the current node. If a collision exists, return to Step 332 to re-select the current node. If no collision exists, add the current node to the non-collision node list and continue to the next step; Step 334: Detect the distance between the current node and the end point. If the distance is less than the distance threshold, jump to Step 337; otherwise, continue to the next step; Step 335: Determine the adjacent nodes of the current node and calculate a temporary cost temp for each adjacent node; Step 336: For each adjacent node, determine whether it is in the g-value list. If it is, compare its temporary cost temp with the cumulative cost g saved in the g-value list. If temp < g, update the cumulative cost g corresponding to this adjacent node in the g-value list, calculate its combined cost f, and update the parent-child relationship between the current node and this adjacent node. For each adjacent node, determine whether it is in the open list. If it is not in the open list, or if it is in the open list and its temporary cost temp is less than its actual cumulative cost g, set the current node as its parent node, move it into the open list, update the cumulative cost g corresponding to this adjacent node in the g-value list, and calculate its combined cost f; return to Step 332; Step 337: Access the parent node of each node in turn from the end point until backtracking to the start point to obtain a preliminary optimized path.

9. The fracture reduction path planning method according to claim 8, characterized in that, The overall cost f is calculated based on the evaluation function f(x), where f(x) = g(x) + w. h(x), where x represents a node, g(x) represents the cumulative cost function used to calculate the actual cumulative cost from the starting point to node x, and h(x) represents the heuristic function used to calculate the estimated cost from node x to the end point; The temporary cost temp = g(x) + cost(x, neighbor), where cost represents the cost of moving from node x to the adjacent node neighbor.

10. A fracture reduction path planning device, characterized in that, It includes: An attitude setting module for determining the initial pose and the reset target pose of the fracture fragment; The initial reset path acquisition module is used to create a forward random expansion tree and a backward random expansion tree based on the initial pose and the reset target pose, and to achieve this through RRT. The Connect algorithm performs bidirectional expansion to obtain the initial reset path; The path optimization module is used to improve the BIT based on the constraint space determined according to the initial reset path. The algorithm iteratively optimizes the initial reset path to obtain an optimized path.

Images